The equation for inverse function g^{-1} (x) text{for the function} g (x) = sqrt{x + 2}.

necessaryh

necessaryh

Answered question

2020-12-29

The equation for inverse function g1(x) for the function g(x)=x + 2.

Answer & Explanation

Pohanginah

Pohanginah

Skilled2020-12-30Added 96 answers

Consider the function,
g(x)=x+2.
The function g(x)=x+2. it is the same function if
x0andg(x)>0.
In order to find the inverse of a function, first replzce g(x) by y.
y=x+2
Now, interchange x and y,
x=y+2
To simplify the above equation further, use the formula, if mx=n, then
m=±nx,
where n and m are positive real numbers, n  0 and x is the positive integer,
x2=y + 2
y=x2  2
Thus, change y by g1(x).
g1(x)=x2  2 for x0
Therefore, the inverse of the given function g(x)=x+2isg01(x)=x22 for
x0
Use the transformation of the graph of the parent function h(x)=x to graph the given function g(x)=x+2.
Draw the graph of the parent function h(x)=x.
Plot the graph of h(x)=x
image
Consider the original function g(x)=x + 2.
Use the properties of the transformation of the graph. In the graph of the function g(x)=x + 2the parent function gtaph h(x)=x is shifted to 2 unit towards the left along the abscissa.
Hence, the grapg for the function g(x)=x + 2 is
image
Similarly, using the transformation of the graphs, plot the graph of the inverse function
g1(x)=x2  2 for the restriction x  0.
image
It can be observed that the curve of the inverse function g1(x)=x2  2 for the restriction x  0
and the function g(x)=x + 2 are symmetric with respect to the line y=x.

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